We have discovered several new features of the mechanism of the site-specific recombination that integrates the DNA of the bacterial virus lambda into the chromosome of its E. coli host. We showed that the two strand-exchanges that comprise the crossover not only are separated in time and space but have a fixed order. We have determined that this polarity is dictated not by local DNA sequence preferences but by the global structure of the synaptic complex. We have initiated a kinetic study of recombination by determining the dependence of the rate of the reaction upon the concentration of one of the DNA species. An accessory factor is needed for efficient recombination; we have shown that this protein causes bending of DNA upon binding.